Factor the trinomial completely. \[ x^{2}+6 x+8 \]

To factor the quadratic trinomial \( x^{2} + 6x + 8 \) completely, follow these steps: 1. **Identify the coefficients:** - The quadratic trinomial is of the form \( ax^{2} + bx + c \), where: - \( a = 1 \) - \( b = 6 \) - \( c = 8 \) 2. **Find two numbers that multiply to \( c \) (which is 8) and add up to \( b \) (which is 6):** - Consider the pairs of factors of 8: - \( 1 \times 8 = 8 \) (sum is 9) - \( 2 \times 4 = 8 \) (sum is 6) - The pair \( 2 \) and \( 4 \) add up to \( 6 \), which is the coefficient of the middle term. 3. **Write the factored form:** - Using the numbers \( 2 \) and \( 4 \), the trinomial can be factored as: \[ (x + 2)(x + 4) \] **Final Answer:** \[ (x + 2)(x + 4) \]